What are similar shapes? Real life examples on similar shapes.

Updated on July 17, 2010

Two shapes are said to be similar if the all the sides of
both shapes have been enlarged by the same scale factor. So all you need to do
is work out the scale factors for the corresponding sides and if they are equal
then the two shapes will be similar. Let’s take a look at a few examples:

Example 1

A small picture frame has a length of 5 inches and a height
of 3 inches. A larger picture frame has length of 15 inches and a height of 9
inches. Prove that the two picture frames are similar shapes.

Length scale factor:

15 ÷ 5 = 3

Height scale factor:

9 ÷ 3 = 3

So the two picture frames are similar as both
lengths have
the same scale factor.

Example 2

A small window has a base length of 0.5m and a
height of
0.75m. A larger window has a base length of 1.2m and a height of 1.5m.
Are the
two windows similar shapes?

Base length scale factor:

1.2 ÷ 05 = 2.4

Height scale factor:

1.5 ÷ 0.75 = 2

Since the scale factors are different then the two
windows
are not similar shapes.

Example 3

A bank note has a length of 140mm and a width of
50mm. A
slightly larger bank note has a length of 182mm and a width of 65mm. Are
the
two bank notes similar rectangles.

Length scale factor:

182 ÷ 140 = 1.3

Width scale factor:

65 ÷ 50 = 1.3

Since the bank notes have been enlarged by the same
scale
factor then the two bank notes are similar shapes.

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